Vol. 7, 1921 
GENETICS: T. ELLINGER 
137 
with age to a certain point followed by a decline. An empirical curve 
following these plotted points shows a type familiar to us from other bi- 
ological problems. It is in fact a logarithmic curve. Pearl 17 has shown 
that the changes in milk flow with age in dairy cattle follow such a loga- 
rithmic curve and he has determined its equation. 
The writer has now proceeded to form the equation relating fertility to 
to age in the material at hand, and has in the calculations used the method 
of moments (Miner 13 ). 
The general form of the equation is 
y = a + bx + cx 2 + d log x 
where y denotes the size of litter and x the ordinal litter number. 
In this special case the equation has been calculated to be the following 
;y = 8.414 + 0.915* - 0.078* 2 + 1.627 log*. 
By solving the equation for the values of x ranging from 1 to 10 the theo- 
retical average size of the successive litters has been determined. These 
values are given in the third column of table 1 and they are used in plotting 
the curve in figure 1 . This curve shows a satisfactory agreement with the 
empirical figures plotted out. 
By putting dy/dx = 0 and solving for x the litter of maximum 
size is found to be 6.56th in order. 
Summary. — 1. Records from 134 sows of native Danish breed all having 
ten litters to their credit show an increase in fertility up to the 6.56 point 
in litter order followed by a decrease. 
2. The curve relating fertility to age is logarithmic, its equation is calcu- 
lated, and the curve fitted. 
Papers from the Department of Biometry and Vital Statistics, School of Hygiene 
and Public Health, Johns Hopkins University, No. 35. 
2 The native Danish breed is a white, fertile and hardy hog of bacon type, producing 
sometimes crossed with Yorkshire boars — the great proportion of the choice bacon 
exported from Denmark to England. 
3 Bell, A. G. 1904. The multi-nippled sheep of Beinn Bhreagh. Science, N. S., 19. 
4 Bell, A. G. 1912. Sheep breeding experiments on Beinn Bhreagh. Ibid., 34. 
5 Carmichael, W. J. and John B. Rice. 1920. Variation in farrow: With special 
reference to birth weight of pigs. Univ. Illinois, Agric. Exp. Sta., Bull. 226. 
6 Carlyle, W. L. and T. F. Mc Connell. 1902. Some observations on sheep breeding 
from the Experiment Stations flock records. Univ. Wisconsin, Agric. Exp. Sta., Bull. 
95. 
7 Fr6lich und Georgs. 1911. Fruchtbarkeit und Geschlechtverhaltnis beim weissen 
Edelschwein. Jahrbuch fur wissenschaftliche und praktische Tierzucht, 6. 
8 Hammond, John. 1914. On some factors controlling fertility in domestic animals. 
J. Agric. Sci., 6. 
9 Humphrey, G. C. and F. Kleinheinz. 1907. Observations on sheep breeding 
from records of the university flock. 24th Ann. Rep. Wisconsin Agric. Exp. Sta. 
10 Jones, S. N. H. and J. E- Rouse. 1920. The relation of dam to observed fecundity 
in domestic animals. I. Multiple birth in cattle and sheep. Dairy Sci., 3. 
